Spent some time down there hunting coues deer, we were about 30 minutes from Tombstone. There is alot of private land, but from what I heard, some of the ranchers will let you on if you ask.
I would bet the area around the San Pedro would support some good mule deer. I think the drought has hit the area harder than others. I would recomend getting a map of 30b from the AZ game and fish (one of the few they have).
Good Luck.